HANKEL

Purpose:

Generates a Hankel matrix.

Syntax:

HANKEL(c, r)

c	-	A series, the first column of the output array.
r	-	Optional. A series, the last row of the output array. If not specified, the first element of the last row equals the last column value and the remaining values are all 0.

Returns:

An array, a Hankel matrix.

Example:

c = {1, 2, 3};

h = hankel(c);

h == {{1, 2, 3},

{2, 3, 0},

{3, 0, 0}}

The first row and column of h is identical to c.

Example:

c = {1, 2, 3};

r = {3, 8, 9};

h = hankel(c, r);

h == {{1, 2, 3},

{2, 3, 8},

{3, 8, 9}}

The last row is identical to r and the first column is identical to c.

Remarks:

For column c and row r, a Hankel matrix takes the form:

c[1] c[2] c[3] ... r[1]

c[2] r[1] r[1] ... r[2]

c[3] r[2] r[2] ... r[3]

. . . . .

c[n] r[n-2] r[n-1] ... r[n]

If r is not specified, a square Hankel matrix is returned where c represents the first row and column. The elements below the first anti-diagonal are zero such that:

If r is specified, an unsymmetric Hankel matrix is returned where the first column is c and the last row is r such that:

In this case, if c[end] ≠ r[1], c[end] is used as the last element.

HANKEL

Purpose:

Syntax:

Returns:

Example:

Example:

Remarks:

See Also: